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Scalarized solutions of set-valued optimization problems and generalized variational-like inequalities

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In this paper by using the scalariation method we introduced the concept of relaxed K-preinvex set-valued maps and obtain some equivalence results of them in terms of normal subdifferential. Also,… Click to show full abstract

In this paper by using the scalariation method we introduced the concept of relaxed K-preinvex set-valued maps and obtain some equivalence results of them in terms of normal subdifferential. Also, we consider generalized Minty variational-like inequalities and show that the set of solutions is equal to scalarized set-valued  optimization problems’s solutions under generalized relaxed convexity assumptions.

Keywords: like inequalities; valued optimization; variational like; set valued; optimization problems

Journal Title: Filomat
Year Published: 2017

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